The analysis of the results of the Neutrino-4 experiment on search for sterile neutrino and comparison with results of other experiments А.P. Serebrov, R.M. Samoilov, NRC “KI” Petersburg Nuclear Physics Institute, Gatchinа, Russia E-mail: [email protected] Abstract We present new results of measurements of reactor antineutrino flux and spectrum dependence on the distance in the range 6-12 meters from the center of the reactor core. Additional measurements were carried out and set of data to perform statistical analysis was almost doubled since the previous report. 2 Using all collected data, we performed the model independent analysis on the oscillation parameters ∆m14 2 and sin 2휃14. The method of coherent summation of results of measurements allows us to directly observe 2 the effect of oscillations. We observed an oscillation effect in vicinity of Δm14 = (7.25 ± 0.13푠푡푎푡 ± 2 2 1.08푠푦푠푡 )eV and sin 2휃 = 0.26 ± 0.08푠푡푎푡 ± 0.05푠푦푠푡. We provide a comparison of our results with results of other experiments on search for sterile neutrino. Combining the result of the Neutrino-4 experiment and the results of measurements of the gallium anomaly and reactor anomaly we obtained 2 value sin 2θ14 ≈ 0.19 ± 0.04 (4.6σ). Also was performed comparison of Neutrino-4 experimental results with results of other reactor experiments NEOS, DANSS, STEREO, PROSPECT and accelerator experiments MiniBooNE, LSND and IceCube experiment. Mass of sterile neutrino obtained from data collected in the Neutrino-4 experiment (in assumption 2 2 m4 ≈ Δm14) is m4 = 2.68 ± 0.13eV. Using the estimations of mixing angles obtained in other experiments and our new results we can calculate, within 3+1 neutrino model, masses of electron, muon, eff eff eff and tau neutrinos: m휈푒 = (0.58 ± 0.09)eV, m휈휇 = (0.42 ± 0.24)eV, m휈휏 ≤ 0.65eV. Extended PMNS matrix for (3 + 1) model with one sterile neutrino is provided, neutrino flavor mixing scheme with sterile neutrino and global fit of reactor experiments. 1. Introduction Experimental search for possible existence of neutrino oscillation into sterile state have been carried out for many years. That idea is under consideration in experiments carried out at accelerators, reactors, and artificial neutrino sources [1-23]. Sterile neutrino can be considered as a candidate for the dark matter. The hypothesis of oscillation can be verified by direct measurement of the antineutrino flux and energy spectrum vs. distance at short 6 – 12m distances from the reactor core. We use method of relative measurements, which can be more precise. It requires a detector to be movable and spectrum sensitive. To detect oscillations to a sterile state, one needs to observe a deviation of flux-distance relation from 1/L2 dependence and alteration of the form of energy spectrum with distance. If such process does occur, it can be described at short distances by the equation: 2 2 2 2 ∆m14[eV ]L[m] P(ν̅e → ν̅e) = 1 − sin 2θ14 sin (1.27 ) (1) Eν̅[MeV] 2 where 퐸휈̅ is antineutrino energy in MeV, L – distance in meters, ∆m14 is difference between squared masses of electron and sterile neutrinos, 휃14 is mixing angle of electron and sterile neutrinos. For the experiment to be conducted, one needs to carry out measurements of the antineutrino flux and spectrum as near as possible to a practically point-like antineutrino source. 2. Detector design The detector scheme with active and passive shielding is shown in fig. 1. The liquid scintillator detector has volume of 1.8 m3 (5x10 sections having size of 0.225x0.225x0.85m3, filled with scintillator to the height of 70 cm). Scintillator with gadolinium concentration 0.1% was used in detector to register + inverse beta decay (IBD) events ν̅e + p → e + n. The method of antineutrino registration is to select a correlated pare of signals: prompt positron signal and delayed signal of neutron captured by gadolinium. The neutrino detector active shielding consists of external and internal parts relative to passive shielding. The internal active shielding is located on the top of the detector and under it. The detector has a sectional structure. It consists of 50 sections – ten rows with 5 sections in each. The first and last detector rows were also used as an active shielding and at the same time as a passive shielding from the fast neutrons. Thus, the fiducial volume of the scintillator is 1.42 m3. For carrying out measurements, the detector has been moved to various positions at the distances divisible by section size. As a result, different sections can be placed at the same coordinates with respect to the reactor except for the edges at closest and farthest positions. Fig. 1. General scheme of an experimental setup. 1 – detector of reactor antineutrino, 2 – internal active shielding, 3 – external active shielding (umbrella), 4 – steel and lead passive shielding, 5 – borated polyethylene passive shielding, 6 – moveable platform, 7 – feed screw, 8 – step motor, 9 – shielding against fast neutrons made of iron shot. The measurements of fast neutrons and gamma fluxes in dependence on distance and reactor power were made before installing the detector into passive shielding [24]. Absence of noticeable dependence of the background on both distance and reactor power was observed. As a result, we consider that difference in signals (reactor ON - reactor OFF) appears mostly due to antineutrino flux from operating reactor. The signal generated by fast neutrons from reactor does not exceed 3% of the neutrino signal. The fast neutron background is formed by cosmic rays. The averaged over distance ratio of ON-OFF (antineutrino) signals to background is 0.5. 3. Measurements – the scheme of reactor operation and detector movements The measurements with reactor under operation have started in June 2016 and were continued till June 2019, when reactor was stopped for renovation. From June 2019 till January 2020 the background has been measured. Measurements with the reactor ON were carried out for 720 days, and with the reactor OFF- for 417 days. In total, the reactor was switched on and off 87 times. Measurements from September 2018 to July 2019 were carried out mainly in near positions to the reactor, where the signal to background ratio is significantly better. This measurement schedule made it possible to almost double (in comparison to the first stage of the experiment [24]) the amount of collected data in half the time and thus increase the statistical accuracy of measurements by factor 1.4. The scheme of reactor operation and detector movements is shown in fig. 2 at the top. The ON-OFF difference is 223 events per day in distance range 6 – 9 m. Signal/background ratio is 0.54. To obtain antineutrino spectrum as difference ON-OFF background processes associated with cosmic radiation are subtracted. The measurements of fast neutrons and gamma fluxes in dependence on distance and reactor power were made before installing the detector into passive shielding. Absence of noticeable dependence of the background on both distance and reactor power was observed [24]. As a result, we consider that difference in signals (reactor ON - reactor OFF) appears mostly due to antineutrino flux from operating reactor. Thus, hereinafter ON-OFF count means antineutrino count. Fig. 2. Top - scheme of detector operation and detector movements; bottom - the distribution of deviations from average value of correlated events rates differences (ON-OFF) normalized on their statistical uncertainties. The measurements of the background (OFF) and measurements with reactor in operation mode (ON) were carried out for each detector position within single measuring period. A reactor cycle is 8-10 days long. Reactor shutdowns are 2-5 days long and usually alternates (2-5-2-...). The reactor shutdowns in summer for a long period for scheduled preventive maintenance. The movement of the detector to the next measuring position takes place in the middle of reactor operational cycle. The stability of the results of measurements is characterized by distributions of ON-OFF difference fluctuations normalized on their statistical uncertainties, in measurements within one measuring period. The distribution is shown in fig.2 at the bottom. That distribution has the form of normal distribution, but its width exceeds unit by (7±4)%. This is a result of additional dispersion which appears due to fluctuations of cosmic background and impossibility of simultaneous measurements of the effect and background. 4. The matrix of measurements of the antineutrino flux dependence on distance and energy The results of experimental measurements of the antineurino flux dependence on distance and energy of antineurino can be presented in the form of a matrix, which contains 216 elements, where 푁푖푘 is difference of ON - OFF rates for i-th interval of energy and for k-th distance from reactor core. The energy spectrum is divided into 9 intervals of 500 keV, which corresponds to the energy resolution of the detector ±250 keV. The distnce step corresponds to the cell size of 23cm. In total there are 24 positions of antineurino flux measurements from 6.4m to 11.9m. Also more detailed data representations with devision into energy intervals 125keV and 250 keV were used. 5. Scheme of the experimental data analysis There is a well-known problem of discrepancy between the experimental and calculated spectra, which also manifests itself in our experiment [23]. Therefore, method of the analysis of the experimental data should not rely on precise knowledge of the energy spectrum. Therefore, we propose model-independent method of data analysis, which employs equation (2), where the numerator is the rate of antineutrino events per 105 s with a correction to geometric factor L2 and denominator is the antineutrino events rate averaged over all distances: 2 2 2 1.27Δ푚14퐿푘 (1−sin 2휃14 sin ( )) 2 −1 퐾 2 퐸푖 (푁푖푘 ± Δ푁푖푘)퐿푘⁄퐾 ∑푘 (푁푖푘 ± Δ푁푖푘)퐿푘 = 2 (2) −1 퐾 2 2 1.27Δ푚14퐿푘 퐾 ∑푘 (1−sin 2휃14 sin ( )) 퐸푖 Equation (2) can be used to model-independent analysis of data because the left part includes only experimental data 푘 = 1, 2, … 퐾 for all distances in the range 6.4-11.9 m, 퐾 = 24; 푖 = 1, 2, … 9 corresponding to 500 keV energy intervals in range 1.5 MeV to 6.0 MeV.